He needed a bit of help when going through the flats, but otherwise did everything on his own. It's interesting to see how he learns to navigate the terrain (steeper vs flatter sections). I didn't teach him to do that, but he figured out pretty much on his own that he can go parallel on flatter sections but needs the snowplough on steeper ones. An alternative would be to complete the turns to control the speed. I would need to ski in front of him to show him the way, that's probably our next step.
Lots to be proud of, Dad! Your son is clearly having a blast skiing, and that's all to your credit. He seems to be willing to take instruction well, also kudos to you. What a great time in life.
Looks like it's time for that bolded part now. Lead him. Lead him all the time for a while. When you're leading, show him how he can slow down by pointing his "arrow" (the wedge) at the trees between all his turns. Do this on low pitch terrain where he slows down too much when he does this. Do it enough so he gets deeply aware that going across the hill in that wedge slows him down, even to a point where he needs to "walk" to keep going. Go ahead and have him walk at first.
Then start teaching him to skate during that slow part. Between turns on low pitch terrain is a great time to work on skating. Can he catch up with you between turns by skating? Can he even tag your coat with his uphill/inside hand, the one he is raising, by skating up to you? Spend time working on his skating while playing tag between turns. This can be a fun game.
Then, staying on that low pitch terrain, show him how going across the slope with skis parallel helps him keep up his speed during that part of the sequence. Lead. Work on that low pitch terrain for a few ski days with him behind you, pointing his skis at the trees between turns and either skating or going parallel, until he's very good at getting his skis parallel between all his turns. You'll want him to want to go parallel because the walking is getting frustrating and the skating is exhausting. Your goal is for him to easily switch from parallel to wedge and back to parallel with each turn, and on occasion from wedge or parallel to diverging tips for skating. Gaining that agility with how the skis point is great at this age.
Once he can do that, there are some steps beyond that which should get him parallel. People here will have lots of suggestions for working on getting to parallel. Right now he goes into a very wide wedge to control his speed on steeper terrain and you want to nip that in the bud. If that wide wedge for controlling speed gets deeply embedded, it will be very difficult to purge. Completing turns is the way to control speed, not the width of the wedge. Teaching him that is your next goal.
He can probably lose the arm raise too. It doesn't look like it's doing much for his turns, the leaning-in he was previously doing looks like it's gone, and since the arm raise is no longer functional its timing is getting a little wonky. Delete it as long as the leaning-in doesn't come back.